Question

The distance between the Sun and the Earth is 1 astronomical unit (1 AU). Jupiter takes about 11.9 Earth years to orbit around the Sun. The distance between the Sun and Jupiter, in AU, is about:

• A. \( 3.5 \)
• B. \( 5.2 \)
• C. \( 11.9 \)
• D. \( 7.2 \)

Hint:

Kepler’s third law states that the square of a planet’s orbital period is proportional to the cube of its semi-major axis.

Answer 1

The Correct Option is B

Using Kepler’s third law:
\[ T^2 \propto R^3 \] \[ \left( \frac{T_J}{T_E} \right)^2 = \left( \frac{R_J}{R_E} \right)^3 \] Given \( T_J = 11.9 \) years and \( T_E = 1 \) year:
\[ (11.9)^2 = R_J^3 \] \[ R_J \approx 5.2 AU \]